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I 



THE EINSTEIN THEORY 
OF RELATIVITY 



ARIHUK B. DENNY. 



The Einstein Theory 
of Relativity 

A CONCISE STATEMENT 



Prof. H. A. LORENTZ 

of the University of Lefden 



NEW YORK 
BEENTANO'S 



TyL. GOO. 20.3 
6 ^ Fr 




7u *W. /tW^V vt V V4U< 



VVCtA/ 



Copyright, 1920, by 
BRENTANO'S 



NOTE 

Whether it is true or not that not 
more than twelve persons in all the 
world are able to understand Ein- 
stein's Theory, it is nevertheless a 
fact that there is a constant de- 
mand for information about this 
much-debated topic of relativity. 
The books published on the subject 
are so technical that only a person 
trained in pure physics and higher 
mathemathics is able to fully under- 
stand them. In order to make a 
popular explanation of this far- 
reaching theory available, the pres- 
ent book is published. 

Professor Lorentz is credited by 
Einstein with sharing the develop- 
ment of his theory. He is doubtless 

[6] 



better able than any other man — 
except the author himself — to ex- 
plain this scientific discovery. 

The publishers wish to acknowl- 
edge their indebtedness to the New 
York Times, The Review of Reviews 
and The Athenaev/m for courteous 
permission to reprint articles from 
their pages. Professor Lorentz's 
article appeared originally in The 
Nieuwe Rotterdamsche Courant of 
November 19, 1919. 



[6] 



INTRODUCTION 

The action of the Royal Society at 
its meeting in London on November 
6, in recognizing Dr. Albert Ein- 
stein's " theory of relativity " has 
caused a great stir in scientific cir- 
cles on both sides of the Atlantic. 
Dr. Einstein propounded his theory 
nearly fifteen years ago. The pres- 
ent revival of interest in it is due to 
the remarkable confirmation which 
it received in the report of the ob- 
servations made during the sun's 
eclipse of last May to determine 
whether rays of light passing close 
to the sun are deflected from their 
course. 

The actual deflection of the rays 
that was discovered by the astron- 

[7] 



THE EINSTEIN THEORY 

omers was precisely what had been 
predicted theoreticaUy by Einstein 
many years since. This striking 
confirmation has led certain German 
scientists to assert that no scientific 
discovery of such importance has 
been made since Newton's theory 
of gravitation was promulgated. 
This suggestion, however, was put 
aside by Dr. Einstein himself when 
he was interviewed by a correspond- 
ent of the New York Times at his 
home in Berlin. To this corre- 
spondent he expressed the difference 
between his conception and the law 
of gravitation in the foUowing 
terms: 

" Please imagine the earth re- 
moved, and in its place suspended 
a box as big as a room or a whole 
house, and inside a man naturally 

[8] 



THE EINSTEIN THEORY 

floating in the center, there being 
no force whatever pulling him. Im- 
agine, further, this box being, by a 
rope or other contrivance, suddenly 
jerked to one side, which is scien- 
tifically termed ' difform motion,' as 
opposed to ' uniform motion/ The 
person would then naturally reach 
bottom on the opposite side. The 
result would consequently be the 
same as if he obeyed Newton's law 
of gravitation, while, in fact, there 
is no gravitation exerted whatever, 
which proves thai difform motion 
will in every case produce the same 
effects as gravitation. 

" I have applied this new idea to 
every kind of difform motion and 
have thus developed mathematical 
formulas which I am convinced give 
more precise results than those 

[9] 



THE EINSTEIN THEORY 

based on Newton's theory. New- 
ton's formulas, however, are such 
close approximations that it was dif- 
ficult to find by observation any ob- 
vious disagreement with experi- 



ence." 



Dr. Einstein, it must be remem- 
bered, is a physicist and not an 
astronomer. He developed his the- 
ory as a mathematical formula. 
The confirmation of it came from 
the astronomers. As he himself 
says, the crucial test was supplied 
by the last total solar eclipse. Ob- 
servations then proved that the rays 
of fixed stars, having to pass close 
to the sun to readi the earth, were 
deflected the exact amount de- 
manded by Einstein's formulas. The 
deflection was also in the direction 
predicted by him. 

[10] 



THE EINSTEIN THEORY 

The question must have occurred 
to many, what has all this to do 
with relativity? When this query- 
was propounded by the Times cor- 
respondent to Dr. Einstein he re- 
plied as follows: 

"The term relativity refers to 
time and space. According to Gali- 
leo and Newton, time and space 
were absolute entities, and ttie mov- 
ing systems of the universe were de- 
pendent on this absolute time and 
space. On this conception was built 
the science of mechanics. The re- 
sulting formulas sufficed for all mo- 
tions of a slow nature; it was found, 
however, that they would not con- 
form to the rapid motions appar- 
ent in electrodynamics. 

"This led the Dutch professor, 
Lorentz, and myself to develop the 

[11] 



THE EINSTEIN THEORY 

theory of special relativity. Briefly, 
it discards absolute time and space 
and makes them in every instance 
relative to movi« systeJ By this 
theory all phenomena in electro- 
dynamics, as well as mechanics, 
hitherto irreducible by the old for- 
mulae — ^and there are multitudes — 
were satisfactorily explained. 

J- " Till now it was believed that 
time and space existed by them- 
selves, even if there was nothing 
else — ^no sun, no earth, no stars — 
while now we know that time and 
space are not the vessel for the uni- 
verse, but could not exist at all if 
there were no contents, namely, no 

N^ sun, earth and other celestial bodies. 

" This special relativity, forming 

the first part of my theory, relates 

to all systems moving with uniform 

[12] 



THE EINSTEIN THEORY 

motion; that is, moving in a straight 
line with equal velocity. 

" Gradually I was led to the idea, 
seeming a very paradox in science, 
that it might apply equally to all 
moving systems, even of diffonn 
motion, and thus I developed the 
conception of general relativity 
which forms the second part of my 
theory." 

As sunmiarized by an American 
astronomer, Professor Henry Nor- 
ris Russell, of Princeton, in the 
Scientific American for November 
29, Einstein's contribution amounts 
to this: 

" The central fact which has been 
proved — ^and which is of great inter- 
est and importence — ^is that the na- 
tural phenomena involving gravita- 
tion and inertia (such as the mo- 

[18] 



THE EINSTEIN THEORY 

tions of the planets) and the phe- 
nomena involving electricity and 
magnetism (including the motion of 
light) are not independent of one 
another, but are intimately related, 
so that both sets of phenomena 
should be regarded as parts of one 
vast system, embracing all Nature. 
The relation of the two is, however, 
of such a character that it is per- 
ceptible only in a very few in- 
stances, and then only to refined 
observations/' 

Already before the war, Einstein 
had immense fame among physicists, 
and among all who are interested in 
the philosophy of science, because of 
his principle of relativity. 

Clerk Maxwell had shown that 
light is electromagnetic, and had re- 
duced the whole theory of electro- 

[14] 



THE EINSTEIN THEORY 

magnetism to a small number of 
equations, which are fundamental in 
all subsequent work. But these equa- 
tions were entangled with the hypo- 
thesis of the ether, and with the no- 
tion of motion relative to the etiher. 
Since the ether was supposed to be 
at rest, such motion was indistin- 
guishable from absolute motion. 
The motion of the earth relatively to 
the ether should have been different 
at different points of its orbit, and 
measurable phenomena should have 
resulted from this difference. But 
none did, and all attempts to detect 
effects of motions relative to the 
ether failed. The theory of relativ- 
ity succeeded in accoimting for this 
fact. But it was necessary incident- 
ally to throw over the one universal 
time, and substitute local times at- 

[15] 



THE EINSTEIN THEORY 

tached to moving bodies and varying 
according to their motion. The 
equations on which the theory of re- 
lativity is based are due to Lorentz, 
but Einstein connected them with his 
general principle, namely, that there 
must be nothing, in observable phe- 
nomena, which could be attributed to 
absolute motion of the observer. 

In orthodox Newtonian dynamics 
the principle of relativity had a sim- 
pler form, which did not require the 
substitution of local time for general 
time. But it now appeared that 
Newtonian dynamics is only valid 
when we confine ourselves to veloci- 
ties much less than that of light. 
The whole Galileo-Newton system 
thus sank to the level of a first ap- 
proximation, becoming progressively 
less exact as the velocities concerned 
approached that of light. 

[16] 



THE EINSTEIN THEORY 

Einstein's extension of his prin- 
ciple so as to account for gravitation 
was made during the war, and for a 
considerable period our astronomers 
were unable to become acquainted 
with it, owing to the difficulty of ob- 
taining German printed matter. 
However, copies of his work ulti- 
mately reached the outside world and 
enabled people to learn more about 
it. Gravitation, ever since Newton, 
had remained isolated from other 
forces in nature ; various attempts had 
been made to account for it, but with- 
out success. The immense unifica- 
tion effected by electromagnetism ap- 
parently left gravitation out of its 
scope. It seemed that nature had 
presented a challenge to the physi- 
cists which none of them were able 
to meet. 

[17] 



THE EINSTEIN THEORY 

At this point Einstein intervened 
with a hypothesis which, apart alto- 
gether from subsequent verification, 
deserves to rank as one of the great 
monuments of human genius. After 
correcting Newton, it remained to 
correct Euclid, and it was in terms 
of non-Euclidean geometry that he 
stated his new theory. Non-Eucli- 
dean geometry is a study of which 
the primary motive was logical and 
philosophical; few of its promoters 
ever dreamed that it would come to 
be applied in physics. Some of 
Euclid's axioms were felt to be not 
" necessary truths," but mere empiri- 
cal laws; in order to establish this 
view, self -consistent geometries were 
constructed upon assumptions other 
than those of Euclid. In these 
geometries the sum of the angles of 

[18] 



THE EINSTEIN THEORY 

a triangle is not two right angles, and 
the departure from two right angles 
increases as the size of the triangle 
increases. It is often said that in 
non-Euclidean geometry space has a 
curvature, but this way of stating the 
matter is misleading, since it seems 
to imply a fourth dimension, which 
is not implied by these systems. 

Einstein supposes that space is 
Euclidean where it is sufficiently re- 
mote from matter, but that the pres- 
ence of matter causes it to become 
slightly non-Euclidean — the more 
matter there is in the neighborhood, 
the more space will depart from 
Euclid. By the help of this hypo- 
thesis, together with his previous 
theory of relativity, he deduces gravi- 
tation — ^very approximately, but not 
exactly, according to the Newtonian 
law of the inverse square. 

[19] 



c\ a 4V^^ 



THE EINSTEIN THEORY 

The minute differences between 
the effects deduced from his theory 
and those deduced from Newton are 
measurable in certain cases. There 
are, so far, three crucial tests of the 
relative accuracy of the new theory 
and the old. 

(1) The perihelion of Mercury 
^ "'' ' r shows a discrepancy which has long 

puzzled astronomers. This discrep- 
ancy is fuUy accounted for by Ein- 
stein. At the time when he pub- 
lished his theory, this was its only 
experimental verification. 

(2) Modem physicists were will- 
ing to suppose that light might be 
subject to gravitation — i.e., that a 
ray of light passing near a great mass 
like the sun might be deflected to the 
extent to which a particle moving 
with the same velocity would be de- 

[20] 



THE EINSTEIN THEORY 

fleeted according to the orthodox 
theory of gravitation. But Ein- 
stein's theory required that the light 
should be deflected just twice as much 
as this. The matter could only be 
tested during an eclipse among a 
number of bright stars. Fortunately 
a peculiarly favourable eclipse oc- 
curred last year. The results of the 
observations have now been pub- 
lished, and are found to verify Ein- 
stein's prediction. The verification 
is not, of course, quite exact; with 
such delicate observations that was 
not to be expected. In some cases 
the departure is considerable. But 
taking the average of the best series 
of observations, the deflection at the 
sun's limb is found to be 1.98", with 
a probable error of about 6 per cent., 
whereas the deflection calculated by 

[21] 



THE EINSTEIN THEORY 

Einstein's theory should be 1.75". It 
will be noticed that Einstein's theory 
gave a deflection twice as large as 
that predicted by the orthodox the- 
ory, and that the observed deflection 
is slightly larger than Einstein pre- 
dicted. The discrepancy is well with- 
in what might be expected in view 
of the minuteness of the measure- 
ments. It is therefore generally ac- 
knowledged by astronomers that the 
outcome is a triumph for Einstein. 
(3) In the excitement of this sen- 
sational verification, there has been 
a tendency to overlook the third ex- 
perimental test to which Einstein's 
theory was to be subjected. If his 
theory is correct as it stands, there 
ought, in a gravitational field, to be 
a displacement of the lines of the 
spectrum towards the red. No such 

[22] 



THE EINSTEIN THEORY 

effect has been discovered. Spec- 
troscopists maintain that, so far as 
can be seen at present, there is no 
way of accounting for this failure if 
Einstein's theory m its present form 
is assumed. They admit that some 
compensating cause may be discov- 
ered to explain the discrepancy, but 
they think it far more probable that 
Einstein's theory requires some es- 
sential modification. Meanwhile, a 
certain suspense of judgment is 
called for. The new law has been 
so amazingly successful in two of the 
three tests that there must be some 
thing valid about it, even if it is not 
exactly right as yet. 

Einstein's theory has the very 
highest degree of aesthetic merit: 
every lover of the beautiful must 
wish it to be true. It gives a vast 

[28] 



THE EINSTEIN THEORY 

unified survey of the operations of 
nature, with a technical simplicity in 
the critical assumptions which makes 
the wealth of deductions astonishing. 
It is a case of an advance arrived at 
by pure theory: the whole eflFect of 
Einstein's work is to make physics 
more philosophical (in a good sense) , 
and to restore some of that intellec- 
tual unity which belonged to the 
great scientific systems of the seven- 
teenth and eighteenth centuries, but 
which was lost through increasing 
specialization and the overwhelming 
mass of detailed knowledge. In 
some ways our age is not a good one 
to live in, but for those who are in- 
terested in physics there are great 
compensations. 



[24] 



THE EINSTEIN THEORY 
OF RELATIVITY 

A Concise Statement by Prof. H. A. 
Lorentz, of the University of Ley den 

The total eclipse of the sun of 
May 29, resulted in a striking con- 
firmation of the new theory of the 
universal attractive power of gravi- 
tation developed by Albert Ein- 
stein, and thus reinforced the con- 
viction that the defining of this the- 
ory is one of the most important 
steps ever taken in the domain of 
natural science. In response to a 
request by the editor, I will at- 
tempt to contribute something to its 

[35] 



THE EINSTEIN THEORY 

J 

general appreciation in the follow- 
ing lines. 

For centuries Newton's doctrine 
of the attraction of gravitation has 
been the most prominent example 
of a theory of natural science. 
Through the simplicity of its basic 
idea, an attraction between two 
bodies proportionate to their mass 
and also proportionate to the square 
of the distance; through the com- 
pleteness with which it explained so 
many of the peculiarities in tihe 
movement of the bodies making up 
the solar system; and, finally, 
through its universal validity, even 
in the case of the far-distant plan- 
etary systems, it compelled the ad- 
miration of all. 

But, while the skill of the math- 
ematicians was devoted to making 

[26] 



THE EINSTEIN THEORY 

more exact calculations of the con- 
sequences to which it led, no real 
progress was made in the science of 
gravitation. It is true that the in- 
quiry was transferred to the field of 
physics, following Cavendish's suc- 
cess in demonstrating the common 
attraction between bodies with which 
laboratory work can be done, but it 
always was evident that natural 
philosophy had no grip on the uni- 
versal power of attraction. While 
in electric effects an influence exer- 
cised by the matter placed between 
bodies was speedily observed — ^the 
starting-point of a new and fertile 
doctrine of electricity — ^in the case 
of gravitation not a trace of an in- 
fluence exercised by intermediate 
matter could ever be discovered. It 
was, and remained, inaccessible and 

[27] 



THE EINSTEIN THEORY 

unchangeable, without any connec- 
tion, apparently, with other phe- 
nomena of natural philosophy. 

Einstein has put an end to this 
isolation; it is now well established 
that gravitation affects not only 
matter, but also light. Thus 
strengthened in the faith that his 
theory already has inspired, we may 
assume with him that there is not a 
single physical or chemical phe- 
nomenon — ^which does not feel, al- 
though very probably in an unno- 
ticeable degree, the influence of 
gravitation, and that, on the other 
side, the attraction exercised by a 
body is limited in the first place by 
the quantity of matter it contains 
and also, to some degree, by motion 
and by the physical and chemical 
condition in which it moves. 

[28] 



THE EINSTEIN THEORY 

It is comprehensible that a person 
could not have arrived at such a far- 
reaching change of view by continu- 
ing to follow the old beaten paths, 
but only by introducting some sort 
of new idea. Indeed, Einstein ar- 
rived at his theory through a train 
of thought of great originality. Let 
me try to restate it in concise terms. 



[29] 



THE EARTH AS A MOVING 

CAR 

Everyone knows that a person 
may be sitting in any kind of a 
vehicle without noticing its progress, 
so long as the movement does not 
vary in direction or speed; in a car 
of a fast express train objects fall 
in just the same way as in a coach 
that is standing still. Only when 
we look at objects outside the train, 
or when the air can enter the car, do 
we notice indications of the motion. 

We may compare the earth with 
such a moving vehicle, which in its 
course around the sun has a remark- 
able speed, of which the direction 
and velocity during a considerable 
period of time may be regarded as 

[30] 



THE EINSTEIN THEORY 

constant. In place of the air now 
comes, so it was reasoned formerly, 
the ether which fills the spaces of 
the universe and is the carrier of 
light and of electro-magnetic phen- 
omena; there were good reasons to 
assmne that the earth was entirely 
permeable for the ether and could 
travel through it without setting it 
in motion. So here was a case com- 
parable with that of a railroad coach 
open on all sides. There certainly 
should have been a powerful " ether 
wind" blowing through the earth 
and all our instruments, and it was 
to have been expected that some 
signs of it would be noticed in con- 
nection with some experiment or 
other. Every attempt along that 
line, however, has remained fruitless ; 
all the phenomena examined were 

[31] 



THE EINSTEIN THEORY 

evidently independent of the motion 
of the earth. That this is the way they 
do function was brought to the front 
by Einstein in his first or " special " 
theory of relativity. For iL the 
ether does not function and in the 
sketch that he draws of natural 
phenomena there is no mention of 
that intermediate matter. 

If the spaces of the imiverse are 
filled with an ether, let us suppose 
with a substance, in which, aside 
from eventual vibrations and other 
slight movements, there is never any 
crowding or flowing of one part 
alongside of another, then we can 
imagine fixed points existing in it; 
for example, points in a straight 
line, located one meter apart, points 
in a level plain, like the angles or 
squares on a chess board extend- 

[82] 



THE EINSTEIN THEORY 

ing out into infinity, and finally, 
points in space as they are obtained 
by repeatedly shifting that level 
spot a distance of a meter in the 
direction perpendicular to it. If, 
consequently, one of the points is 
chosen as an '' original point " we 
can, proceeding from that point, 
readi any other point through three 
steps in the common perpendicular 
directions in which the points are 
arranged. The figures showing how 
many meters are comprized in each 
of the steps may serve to indicate 
the place reached and to distinguish 
it from any other; these are, as is 
said, the " co-ordinates " of these 
places, comparable, for example, 
with the numbers on a map giving 
the longitude and latitude. Let us 
imagine that each point has noted 

[88] 



THE EINSTEIN THEORY 

upon it the three numhers that give 
its position, then we have something 
comparable with a measure with 
nimibered subdivisions ; only we now 
have to do, one might say, with a 
good many imaginary measures in 
three common perpendicular direc- 
tions. In this " system of co-ordi- 
nates " the numbers that fix the po- 
sition of one or the other of the 
bodies may now be read off at any 
moment. 

This is the means which the as- 
tronomers and their mathematical 
assistants have always used in deal- 
ing with the movement of the heav- 
enly bodies. At a determined mo- 
ment the position of each body is 
fixed by its three co-ordinates. If 
these are given, then one knows also 
the common distances, as well as the 

[84] 



THE EINSTEIN THEORY 

angles formed by the connecting 
lines, and the movement of a planet 
is to be known as soon as one knows 
how its co-ordinates are changing 
from one moment to the other. Thus 
the picture that one forms of the 
phenomena stands there as if it were 
sketched on the canvas of the mo- 
tionless ether. 



[85] 



EINSTEIN'S DEPARTURE 

Since Einstein has cut loose from 
the ether, he lacks this canvas, and 
therewith, at the first glance, also 
loses the possibility of fixing the 
positions of the heavenly bodies and 
mathematically describing their 
movement — i.e., by giving compari- 
sons that define the positions at 
every moment. How Einstein has 
overcome this difiiculty may be 
somewhat elucidated through a sim- 
ple illustration. 

On the surface of the earth the 
attraction of gravitation causes all 
bodies to fall along vertical lines, 
and, indeed, when one omits the re- 
sistance of the air, with an equally 

[86] 



THE EINSTEIN THEORY 

accelerated movement; the velocity 
increases in equal degrees in equal 
consecutive divisions of time at a 
rate that in this country gives the 
velocity attained at the end of a sec- 
ond as 981 centimeters (82.2 feet) 
per second. The number 981 de- 
fines the "acceleration in the field 
of gravitation," and this field is ful- 
ly characterized by that single num- 
ber; with its help we can also cal- 
culate the movement of an object 
hurled out in an arbitrary direction. 
In order to measure the accelera- 
tion we let the body drop alongside 
of a vertical measure set solidly on 
the ground ; on this scale we read at 
every moment the figure that indi- 
cates the height, the only co-ordi- 
nate that is of importance in this 
rectilinear movement. Now we ask 

[87] 



THE EINSTEIN THEORY 

what would we be able to see if the 
measure were not bound solidly to 
the earth, if it, let us suppose, 
moved down or up with the place 
where it is located and where we are 
ourselves. If in this case the speed 
were constant, then, and this is in 
accord with the special theory of re- 
lativity, there would be no motion 
observed at all ; we should again find 
an acceleration of 981 for a falling 
body. It would be different if the 
measure moved with changeable 
velocity. 

If it went down with a constant 
acceleration of 981 itself, then an 
object could remain permanently at 
the same point on the measure, or 
could move up or down itself along- 
side of it, with constant speed. The 
relative movement of the body with 

[38] 



THE EINSTEIN THEORY 

regard to the measure should be 
without acceleration, and if we had 
to judge only by what we observed 
in the spot where we were and 
which was falling itself, then we 
should get the impression that there 
was no gravitation at all. If the 
measure goes down with an accele- 
ration equal to a half or a third of 
what it just was, then the relative 
motion of the body will, of course, 
be accelerated, but we should find 
the increase in velocity per second 
one-half or two-thirds of 981. If, 
finally, we let the measure rise with 
a uniformly accelerated movement, 
then we shall find a greater accele- 
ration than 981 for the body itself. 
Thus we see that we, also when 
the measure is not attached to the 
earth, disregarding its displacement, 

[39] 



THE EINSTEIN THEORY 

may describe the motion of the body 
in respect to the measure always 
in the same way — i.e.^, as one imi- 
formly accelerated, as we ascribe 
now and again a fixed value to the 
acceleration of the sphere of gravi- 
tation, in a particular case the value 
of zero. 

Of course, in the case here under 
consideration the use of a measure 
fixed immovably upon the earth 
should merit all recommendation. 
But in the spaces of the solar sys- 
tem we have, now that we have 
abandoned the ether, no such sup- 
port. We can no longer establish 
a system of co-ordinates, like the one 
just mentioned, in a universal inter- 
mediate matter, and if we were to 
arrive in one way or another at a 
definite system of lines crossing each 

[40] 



THE EINSTEIN THEORY 

other in three directions, then we 
should be able to use just as well 
another similar system that in re- 
spect to the first moves this or that 
way. We should also be able to re- 
model the system of co-ordinates in 
all kinds of ways, for example by 
extension or compression. That in 
all these cases for fixed bodies that 
do not participate in the movement 
or the remodelling of the system 
other co-ordinates will be read off 
again and again is clear. 



[41] 



NEW SYSTEM OR CO-ORDI- 
NATES 

What way Einstein had to follow 
is now apparent. He must— this 
hardly needs to be said — ^in calculat- 
ing definite, particular cases make 
use of a chosen system of co-ordi- 
nates, but as he had no means of 
limiting his choice beforehand and 
in general, he had to reserve full 
liberty of action in this respect. 
Therefore he made it his aim so to 
arrange the theory that, no matter 
how the choice was made, the phe- 
nomena of gravitation, so far as its 
effects and its stimulation by the at- 
tracting bodies are concerned, may 
always be described in the same way 

[42] 



THE EINSTEIN THEORY 

—Le., through comparisons of the 
same general form, as we again and 
again give certain values to the nimi- 
bers that mark the sphere of gravi- 
tation. (For the sake of sim:plifica- 
tion I here disregard the fact that 
Einstein desires that also the way 
in which time is measured and rep- 
resented by figures shall have no 
influence upon the central value of 
the comparisons.) 

Whether this aim could be at- 
tained was a question of mathemati- 
cal inquiry. It really was attained, 
remarkably enough, and, we may 
say, to the surprise of Einstein him- 
self, although at the cost of consid- 
erable simplicity in the mathemati- 
cal form; it appeared necessary for 
the fixation of the field of gravita- 
tion in one or the other point in 

[43] 



THE EINSTEIN THEORY 

space to introduce no fewer than 
ten quantities in the place of the 
one that occurred in the example 
mentioned above. 

In this connection it is of import- 
ance to note that when we exclude 
certain possibilities that would give 
rise to stiU greater intricax^y, the 
form of comparison used by Ein- 
stein to present the theory is the 
only possible one; the principle of 
the freedom of choice in co-ordi- 
nates was the only one by whidi he 
needed to allow himself to be guided. 
Although thus there was no special 
effort made to reach a connection 
with the theory of Newton, it was 
evident, fortunately, at the end of 
the experiment that the connection 
existed. If we avail ourselves of 
the simplifying circumstance that 

[44] 



THE EINSTEIN THEORY 

the velocities of the heavenly bodies 
are slight in comparison with that 
of light, then we can deduce the the- 
ory of Newton from the new the- 
ory, the " miiversal " relativity the- 
ory, as it is called by Einstein. 
Thus all the conclusions based upon 
the Newtonian theory hold good, as 
must naturally be required. But 
now we have got further along. 
The Newtonian theory can no 
longer be regarded as absolutely 
correct in all cases; there are slight 
deviations from it, which, although 
as a rule unnoticeable, once in a 
while fall within the range of ob- 
servation. 

Now, there was a difficulty in 
the movement of the planet Mer- 
cury which could not be solved. 
Even after all the disturbances 

[46] 



THE EINSTEIN THEORY 

caused by the attraction of other 
planets had been taken into account, 
there remained an inexplicable 
phenomenon — i.e., an extremely 
slow turning of the ellipsis described 
by Mercury on its own plane; Le- 
verrier had found that it amounted 
j>4r to forty-three seconds a century. 
Einstein found that, according to 
his formulas, this ' movement must 
really amount to just that much. 
Thus with a single blow he solved 
one of the greatest puzzles of as- 
stronomy. 

Still more remarkable, because it 
has a bearing upon a phenomenon 
which formerly could not be imag- 
ined, is the confirmation of Ein- 
stein's prediction regarding the in- 
fluence of gravitation upon the 

[46] 



THE EINSTEIN THEORY 

course of the rays of light. That 
such an influence must exist is 
taught by a simple examination; we 
have only to turn back for a moment 
to the following comparison in which 
we were just imagining ourselves to 
make our observations. It was noted 
that when the compartment is fall- 
ing with the acceleration of 981 the 
phenomena therein will occur just 
as if there were no attraction of 
gravitation. We can then see an 
object, Ay stand still somewhere in 
open space. A projectile, B, can 
travel with constant speed along a 
horizontal line, without varying 
from it in the slightest. 

A ray of light can do the same; 
everybody will admit that in each 
case, if there is no gravitation, light 

[47] 



THE EINSTEIN THEORY 

will certainly extend itself in a rec- 
tilinear way. If we limit the light 
to a flicker of the slightest duration, 
so that only a little bit, Cy of a ray 
of light arises, or if we fix our at- 
tention upon a single vibration of 
light, Cy while we on the other hand 
give to the projectile, 3?^ a speed 
equal to that of light, then we can 
conclude that B and C in their con- 
tinued motion can always remain 
next to each other. Now if we 
watch all this, not from the movable 
compartment, but from a place on 
the earth, then we shall note the 
usual falling movement of object A, 
which shows us that we have to deal 
with a sphere of gravitation. The 
projectile B will, in a bent path, 
vary more and more from a hori- 
zontal straight line, and the light 

[48] 



THE EINSTEIN THEORY 

will do the same, because if we ob- 
serve the movements from another 
standpoint this can have no effect 
upon the remaining next to each 
other of B and C. 



[49] 



DEFLECTION OF LIGHT 

The bending of a ray of light thus 
described is much too light on the 
surface of the earth to be observed. 
But the attraction of gravitation ex- 
ercised by the sun on its surface is, 
because of its great mass, more than 
twenty-seven times stronger, and a 
ray of light that goes close by the 
superficies of the sun must surely be 
noticeably bent. The rays of a star 
that are seen at a short distance from 
the edge of the sun will, going along 
the sun, deviate so much from the 
original direction that they strike 
the eye of an observer as if they 
came in a straight line from a point 
somewhat further removed than the 
real position of the star from the 
sun. It is at that point that we 

[60] 



THE EINSTEIN THEORY 

think we see the star; so here is a 
seeming displacement from the sun, 
which increases in the measure in 
which the star is observed closer to 
the sun. The Einstein theory- 
teaches that the displacement is in 
inverse proportion to the apparent 
distance of the star from the centre 
of the sun, and that for a star just 
on its edge it will amount to l'^75 
(1.75 seconds). This is approxi- 
mately the thousandth part of the 
apparent diameter of the sun. / ^ > i -i 

Naturally, the phenomenon can 
only be observed when there is a 
total eclipse of the sun; then one 
can take photographs of neighbor- 
ing stars and through comparing 
the plate with a picture of the same 
part of the heavens taken at a time 
when the sun was far removed from 

[61] 



THE EINSTEIN THEORY 

that point the sought-for movement 
to one side may become apparent. 

Thus to put the Einstein theory 
to the test was the principal aim of 
the English expeditions sent out to 
observe the eclipse of May 29, one 
to Prince's Island, off the coast of 
Guinea, and the other to Sobral, 
Brazil. The first-named expedi- 
tion's observers were Eddington and 
Cottingham, those of the second, 
Crommelin and Davidson. The con- 
ditions were especially favorable, for 
a very large number of bright stars 
were shown on the photographic 
plate; the observers at Sobral be- 
ing particularly lucky in having 
good weather. 

The total eclipse lasted five min- 
utes, during four of which it was 
perfectly clear, so that good photo- 

[52] 



THE EINSTEIN THEORY 
graphs could be taken. In the re- 
port issued regarding the results the 
following figures, which are the 
average of the measurements made 
from the seven plates, are given for 
the displacements of seven stars: 

1".02, 0".92, 0".84, 0".58, 0".54, 

0".36, 0".24, whereas, according to 

the theory, the displacements should 

have amounted to: 0".88, 0".80, 

0".75, 0"AO, 0".52, 0".83, 0".20. 

If we consider that, according to 

ust 

ice 

we 

Us- 

iiys 

of 

the 

the 

aU 



THE EINSTEIN THEORY 

the observations together. As the 
last of the displacements given 
above — i.e., 0".24 is , about one- 
eighth of this, we may say that the 
influence of the attraction of the 
sun upon light made itself felt upon 
the ray at a distance eight times re- 
moved from its centre. 

The displacements calculated ac- 
cording to the theory are, just be- 
cause of the way in which they are 
calculated, in inverse proportion to 
the distance to the centre. Now 
that the observed deviations also ac- 
cord with the same rule, it follows 
that they are surely proportionate 
with the calculated displacements. 
The proportion of the first and the 
last observed sidewise movements is 
4.2, and that of the two most ex- 
treme of the calculated nimibers is 
4.4. 

[64] 



THE EINSTEIN THEORY 

This result is of importance, be- 
cause thereby the theory is excluded, 
or at least made extremely improb- 
able, that the phenomenon of re- 
fraction is to be ascribed to a ring 
of vapor surrounding the sun for a 
great distance. Indeed, such a re- 
fraction should cause a deviation in 
the observed direction, and, in or- 
der to produce the displacement of 
one of the stars under observation 
itself a slight proximity of the vapor 
ring should be sufficient, but we 
have every reason to expect that if 
it were merely a question of a mass 
of gas around the sim the diminish- 
ing effect accompanying a removal 
from the sun should manifest itself 
much faster than is really the case. 
We cannot speak with perfect cer- 
tainty here, as all the factors that 

[66] 



THE EINSTEIN THEORY 

might be of influence upon the dis- 
tribution of density in a sun at- 
mosphere are not well enough 
known, but we can surely demon- 
strate that in case one of the gasses 
with which we are acquainted were 
held in equilibrium solely by the in- 
fluence of attraction of iiie sun the 
phenomenon should become much 
less as soon as we got somewhat fur- 
ther from the edge of the sim. If 
the displacement of the first star, 
which amounts to 1.02-seconds were 
to be ascribed to such a mass of gas, 
then the displacement of the second 
must already be entirely inappreci- 
able. 

So far as the absolute extent of 
the displacements is concerned, it 
was found somewhat too great, as 
has been shown by the figures given 

[66] 



THE EINSTEIN THEORY 

above; it also appears from the final 
result to be 1.98 for the edge of the 
sun — i.e., 13 per cent, greater than 
the theoretical value of 1.75. It 
indeed seems that the discrepancies 
may be ascribed to faults in observa- 
tions, which supposition is supported 
by the fact that the observations at 
Prince's Island, which, it is true, 
did not turn out quite as well as 
those mentioned above, gave the re- 
sult, of 1.64, somewhat lower than 
Einstein's figure. 

(The observations made with a 
second instrument at Sobral gave a 
result of 0.93, but the observers are 
of the opinion that because of the 
shifting of the mirror which re- 
flected the rays no value is to be 
attached to it.) 

[67] 



DIFFICULTY EXAG- 
GERATED 

During a discussion of the results 
obtained at a joint meeting of the 
Royal Society and the Royal As- 
tronomical Society held especially 
for that purpose recently in Lon- 
don, it was the general opinion that 
Einstein's prediction might be re- 
garded as justified, and warm tri- 
butes to his genius were made on 
all sides. Nevertheless, I cannot re- 
frain, while I am mentioning it, 
from expressing my surprise that, 
according to the report in The 
Times, there should be so much com- 
plaint about the difficulty of under- 
standing the new theory. It is evi- 
dent that Einstein's little book 

[68] 



THE EINSTEIN THEORY 

"About the Special and the Gen- 
eral Theory of Relativity in Plain 
Terms," did not find its way into 
England during wartime. Any one 
reading it will, in my opinion, come 
to the conclusion that the basic ideas 
of the theory are really clear and 
simple; it is only to be regretted 
that it was impossible to avoid cloth- 
ing them in pretty involved mathe- 
matical terms, but we must not wor- 
ry about that. 

I allow myself to add that, as 
we follow Einstein, we may retain 
much of what has been formerly 
gained. The Newtonian theory re- 
mains in its full value as the first 
great step, without which one can- 
not imagine the development of as- 
tronomy and without which the sec- 
ond step, that has now been made, 

[69] 



THE EINSTEIN THEORY 

would hardly have been possible. It 
remains, moreover, as the first, and 
in most cases, sufficient, approxi- 
mation. It is true that, according 
to Einstein's theory, because it 
leaves us entirely free as to the way 
in which we wish to represent the 
phenomena, we can imagine an idea 
of the solar system in which the 
planets follow paths of peculiar 
form and the rays of light shine 
along sharply bent lines — think of 
a twisted and distorted planetarium 
— but in every case where we apply 
it to concrete questions we shall so 
arrange it that the planets describe 
almost exact ellipses and the rays of 
light almost straight lines. 

It is not necessary to give up en- 
tirely even the ether. Many natural 
philosophers find satisfaction in the 

[60] 



THE EINSTEIN THEORY 

idea of a material intermediate sub- 
stance in which the vibrations of 
light take place, and they will very 
probably be all the more inclined 
to imagine such a medium when 
they learn that, according to the 
Einstein theory, gravitation itself 
does not spread instantaneously, but 
with a velocity that at the first es- 
timate may be compared with that 
of light. Especially in former years 
were such interpretations current 
and repeated attempts were made 
by speculations about the nature of 
the ether and about the mutations 
and movements that might take 
place in it to arrive at a clear pre- 
sentation of electro-magnetic phe- 
nomena, and also of the functioning 
of gravitation. In my opinion it 
is not impossible that in the future 

[61] 



THE EINSTEIN THEORY 

this road, indeed abandoned at pres- 
ent, will once more be followed with 
good results, if only because it can 
lead to the thinking out of new ex- 
perimental tests. Einstein's theory 
need not keep us from so doing; 
only the ideas about the ether must 
accord with it. 

Nevertheless, even without the 
color and clearness that the ether 
theories and the other models may 
be able to give, and even, we can 
feel it this w^ay, just because of the 
soberness induced by their absence, 
Einstein's work, we may now posi- 
tively expect, will remain a monu- 
ment of science; his theory entirely 
fulfills the first and principal de- 
mand that we may make, that of 
deducing the course of phenomena 
from certain principles exactly and 

[62] 



THE EINSTEIN THEORY 

to the smallest details. It was cer- 
tainly fortunate that he himself put 
the ether in the background; if he 
had not done so, he probably would 
never have come upon the idea that 
has been the foundation of all his 
examinations. 

Thanks to his indefatigable exer- 
tions and perseverance, for he had 
great difficulties to overcome in his 
attempts, Einstein has attained the 
results, which I have tried to sketch, 
while still young; he is now 45 years 
old. He completed his first inves- 
tigations in Switzerland, where he 
first was engaged in the Patent Bu- 
reau at Berne and later as a pro- 
fessor at the Polytechnic in Zurich. 
After having been a professor for 
a short time at the University of 
Prague, he settled in Berlin, where 

[63] 



THE EINSTEIN THEORY 

the Kaiser WiUielm Institute af- 
forded him the opportunity to de- 
vote himself exclusively to his scien- 
tific work. He repeatedly visited 
our country and made his Nether- 
land colleagues, among whom he 
counts many good friends, part- 
ners in his studies and his results. 
He attended the last meeting of the 
department of natural philosophy 
of the Royal Academy of Sciences, 
and the members then had the priv- 
ilege of hearing him explain, in his 
own fascinating, clear and simple 
way, his interpretations of the fim- 
damental questions to which his 
theory gives rise. 



[64] 






• '#• 






/'' 



I